Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 2x + 9$ and $ KL = 3x + 5$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {2x + 9} = {3x + 5}$ Solve for $x$ $ -x = -4$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 2({4}) + 9$ $ KL = 3({4}) + 5$ $ JK = 8 + 9$ $ KL = 12 + 5$ $ JK = 17$ $ KL = 17$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {17} + {17}$ $ JL = 34$